# Stock Price Prediction

Forecasting price movement from historical and alternative data — the canonical example of a low signal-to-noise problem.

**Rests on:** Linear Regression, Stochastic Gradient Descent

*Machine Learning · Machine Learning Foundations*


## Why learn this

Forecasting stock prices is the classic introduction to a core problem in machine learning: extracting a weak signal from noisy data. By mastering this, you learn the discipline of evaluating any predictive model honestly — how to split data so you don't cheat by looking into the future, how to avoid fooling yourself with tests that use future information to predict the past, and why even a perfect model can lose money to transaction costs. These skills carry directly to building systems that forecast demand, detect fraud, predict equipment failure, or recommend content — anywhere the future is uncertain and the data is messy.


## The intuition

Stock price prediction is the art of forecasting tomorrow's price from what happened before. But it's not like predicting the weather where patterns are fairly clear. Stock prices are driven by countless factors — company earnings, investor sentiment, global events, pure randomness — and the information that genuinely moves prices is often tiny compared to the noise. Think of a crowded market: everyone is shouting, and you're trying to hear one quiet voice that knows something. Machine learning tries to find that voice by sifting through historical patterns, but it must be careful not to mistake random noise for a real signal — a mistake that leads to confident but worthless predictions. The central lesson is humility: the market is nearly efficient, meaning most information is already reflected in the price, so the 'signal' you find must be small, fleeting, and easily erased by costs and overfitting.


## An analogy

Predicting stock prices is like trying to guess the next card in a shuffled deck where the deck is being reshuffled constantly. You can study the cards that have already appeared, look for patterns, and even develop a system — but every time you think you've found a pattern, the rules change. Sometimes it seems like red follows black, and you bet on it, but the moment you commit, the deck turns random again. Now imagine you're keeping a diary of your predictions and how they turned out. If you only write down the days you were right and ignore the days you were wrong, you'll think you're a genius. A good data scientist keeps a strict record, testing their rules on days they've never seen before — called out-of-sample data — to see if the pattern holds. The stock market is full of people who built a system that worked in the past, then lost everything when it failed in the future. The same trap awaits the machine learning beginner: your model will look brilliant on the data it was trained on, but that brilliance often evaporates when faced with data it hasn't seen.


## Definition

Stock price prediction is the practice of building a model that forecasts future price movement from historical data (past prices, volumes) and alternative data (news sentiment, economic indicators), while recognizing that the ratio of useful information to random noise is so low that rigorous evaluation using unseen data is the only thing separating a real edge from a lucky test.


## How it connects

This concept connects to the method of splitting data into three distinct groups — training data used to build the model, validation data used to tune it, and testing data used to judge its final accuracy. This sequence prevents cheating by ensuring the model never sees future information. It also relates to linear regression, a basic technique that predicts a value by drawing a straight line through past data points to show how one variable changes with another.


## The mathematics

The mathematics of stock price prediction is built on the branch of probability and statistics, because you are trying to infer a hidden pattern from noisy observations. The core operation is the **mean** — the average — and how it behaves when you look at past prices. But the essential mathematical idea is the **signal-to-noise ratio**: the price movement you want to predict (the signal) is much smaller than the random ups and downs (the noise). A simple prediction model says: tomorrow's price is roughly today's price plus a small random step. This is called a random walk. If you try to predict the step, you're trying to extract a signal that is buried in noise that is ten or a hundred times stronger. The math shows that the best you can do often is predict today's price again. This is why the discipline of evaluation is so important: your model might fit the noise on the training data, but the noise is different on new data, so the model fails. The mathematics also uses the **mean squared error** (MSE): average the squared differences between predicted and actual prices. Squaring makes large errors hurt more, and it gives a single number to minimise.

Let $p_t$ be the price on day $t$. A simple prediction model: $\hat{p}_{t+1} = p_t$ (predict the same price). The error is $e_t = p_{t+1} - \hat{p}_{t+1}$. The Mean Squared Error (MSE) over $n$ days is $\mathrm{MSE} = \frac{1}{n} \sum_{t=1}^{n} e_t^2$. Each symbol is named: $p$ is price, $t$ is the time index (day), $\hat{p}$ is the predicted price, $e$ is the error, $\sum$ means 'add up all these', and $n$ is the number of days.


## A worked example

```
Suppose you have five days of closing prices for a stock (in rupees): 100, 102, 101, 105, 104. You want to predict the price on day 6 using a simple model: predict it as the average of the last two days (a moving average). The actual price on day 6 is 107.

Step 1: Average of last two: (105 + 104) / 2 = 104.5   # We use the two most recent prices to make a prediction.
Step 2: Predicted price for day 6: 104.5   # Our model gives 104.5.
Step 3: Actual price on day 6: 107   # This is the real value.
Step 4: Error: 107 - 104.5 = 2.5   # The model missed by 2.5 rupees.
Step 5: Squared error: 2.5 * 2.5 = 6.25   # Squaring makes the error positive and punishes larger misses.
Step 6: If we did this for many days, the MSE would be the average of all squared errors.   # This gives a single score to compare models.

Result: The MSE on this single day is 6.25. A good model would have a low MSE, but in stock prediction the noise makes any model's MSE large relative to the signal.
```


## From scratch, in Python

```python
import random

# We simulate 10 days of stock prices
daily_prices = [100, 102, 101, 105, 104, 107, 110, 108, 112, 115]

# Step 1: Define a simple prediction function: predict tomorrow = today's price
# This is a function, a reusable block of code. It takes a list of prices and a day index.
def naive_predict(prices, day_index):
    """Predict the next day's price as the current day's price."""
    return prices[day_index]

# Step 2: Use a loop to compute predictions and errors for days 0 to 8
# We can't predict the last day because there is no tomorrow yet.

predictions = []  # empty list to store predictions
errors = []       # empty list to store errors

for day in range(len(daily_prices) - 1):  # loop through days 0,1,...,8
    actual_tomorrow = daily_prices[day + 1]  # the next day's price
    predicted = naive_predict(daily_prices, day)  # today's price
    error = actual_tomorrow - predicted  # difference
    predictions.append(predicted)
    errors.append(error)

# Step 3: Compute the Mean Squared Error
def mean_squared_error(error_list):
    total = 0
    for e in error_list:
        total = total + e * e  # square the error and add to total
    return total / len(error_list)  # divide by count to get the mean

mse = mean_squared_error(errors)
print("Predictions:", predictions)
print("Errors:", errors)
print("Mean Squared Error:", mse)
```


## The same thing, with a framework

```python
In a real system, you'd use a library like scikit-learn or pandas. For example, to compute the moving average forecast you could use `pandas.Series.rolling(window).mean()`, which under the hood does the same summing and dividing you did by hand. A deep learning approach like an LSTM in PyTorch would take sequences of past prices and learn to map them to the next price, but the core idea remains: you compute a prediction, measure the error, and adjust the model's weights to reduce that error. The library abstracts away the loop of drawing samples, but the principle of train and test is still in your hands.
```


## What the code does

The code first creates a list of daily prices. A **list** is a container that keeps things in order, like a queue — you can get the first item, the second, and so on. We define a function `naive_predict` that takes the list of prices and a day index (like a label for the position) and returns the price at that index. Then we use a **loop** (a `for` loop) to go through each day from 0 to 8. For each day, we get the actual price of the next day, predict the next day as today's price, compute the difference (error), and store these in lists. A list can be changed after creation; we `append` to add items to the end. Finally, we define a function `mean_squared_error` that sums the squares of errors and divides by the count to get the average. The output shows the predictions, errors, and the MSE.


## Common misconceptions

**'I can predict the stock market with enough data.'** — If I have years of price data, I can build a model that predicts tomorrow's price with high accuracy.

The market is almost efficient: most public information is already in the price. Any predictable pattern is small and quickly exploited, making it disappear. The signal-to-noise ratio is extremely low — random fluctuations often dwarf any real signal. In fact: Even the best models achieve only a tiny edge over random guessing, and that edge is often less than the transaction costs of acting on it. The goal is to be slightly less wrong, not to be right all the time.

**'A backtest that looks perfect means my model is great.'** — If my model has a 95% accuracy on historical data, it's a sure bet for the future.

Backtests can be overfit — the model may have memorized noise in the training data. Also, if you use a random split that shuffles dates, the model can see future data and 'cheat'. In fact: You must validate on out-of-sample, time-ordered data that the model has never seen. The discipline of a honest backtest is the only way to know if your edge is real.

**'The model is right, the market is wrong.'** — When my model makes a prediction that turns out wrong, it's because the market was irrational, not because my model is flawed.

The market aggregates information from millions of participants; it is not random, but it is noisy. A single wrong prediction is expected; the model's performance should be judged over many predictions, not one. In fact: Evaluate the model statistically over many days, and accept that individual outcomes are mostly noise. A model with a small edge will still be wrong most of the time, but it can be profitable in the long run.

**'I don't need transaction costs — I only need to predict.'** — If I predict the price correctly, I can just buy and sell and make money.

Every trade has a cost — brokerage, taxes, bid-ask spread — and these costs are often larger than the predicted move. A model that predicts a 0.1% rise will lose money after paying 0.2% in costs. In fact: You must subtract transaction costs and slippage from your backtest to see if the strategy is actually profitable. An apparent edge can be erased entirely by these frictions.

**'More data always means a better model.'** — If I train my model on 10 years of data, it will be more accurate than if I use only 1 year.

More data can help, but it also includes more old regimes that may not be relevant today. The market changes — patterns in 2010 may not hold in 2024. Overfitting old noise can make the model worse. In fact: Use a validation set that is recent and representative of the current market. Sometimes a shorter but cleaner period is better than a longer, noisier one.

**'I can use any ML model, as long as it's advanced.'** — A complex deep learning model is always better than a simple linear regression for predicting stock prices.

Stock prices have a very low signal-to-noise ratio. A complex model has many parameters that will fit the noise, leading to overfitting. A simple model like a moving average may do just as well with less risk. In fact: The model's complexity must match the amount of genuine signal. In the presence of high noise, a simple baseline is often the most robust. The default should be earned, not assumed.

**'I need to predict the exact price, not just the direction.'** — To make money, my model must predict the exact closing price tomorrow.

Exact price prediction is nearly impossible due to randomness. The market cares more about whether the price goes up or down, not the exact number. In fact: Focus on predicting the direction of movement or the probability of a certain change. Your model can give a confidence score, and you can act on bets with a positive expected value, not on being exactly right.


## In short

Stock price prediction is the ultimate lesson in humility: the signal is tiny, the noise is huge, and the temptation to fool yourself with overfitted backtests is overwhelming. The key skills are evaluating models honestly — using temporal splits, out-of-sample testing, and accounting for transaction costs — not finding a magic formula. A simple model that survives rigorous validation is worth more than a complex one that dazzles on the training data.


## Where this is used

**In large language models (LLMs):** They are trained to predict the next word, but the same principle of low signal-to-noise appears when they are used for financial analysis. For instance, a system that reads news articles and predicts stock sentiment uses the same evaluation discipline — you must use temporal splits because a model trained on 2023 news would be tested on 2024 news that mentions similar events. The LLM doesn't emerge with a price prediction; rather, it extracts features (sentiment, entity mentions) that then feed into the same regression models you saw in the code. If the LLM is fine-tuned on historical financial data and then evaluated on later data, the risk of overfitting to the noise is just as high, and the temporal split is just as non-negotiable. **In small language models on devices:** A phone that predicts the next word in your typing is not predicting stock prices, but the economics are similar: the model is small, the signal is noisy (language is unpredictable), and the data is limited. The same evaluation problem exists — if you test on a user's previous typing history, the model may appear intelligent but is really memorising. Temporal splits (train on older messages, test on newer) prevent that leakage. **In retrieval-augmented generation (RAG):** When a RAG system retrieves financial documents to answer a user's question about a stock, it is not forecasting prices directly, but it must evaluate its own performance on a question-answering benchmark, and that benchmark must respect temporal order — you can't train on questions from 2024 and then test on 2023 questions. The same overfitting trap applies if the benchmark is not split properly. **In agentic systems that plan and call tools:** An agent that decides when to buy or sell a stock based on price prediction must be evaluated in a simulated environment that includes transaction costs and delays. The backtest overfitting issue is exacerbated because the agent's actions change the data it sees next, creating feedback loops. The system must be trained on time-ordered episodes, not shuffled data, otherwise it learns to exploit leaks that don't exist in live trading. **In everyday applied ML:** Stock prediction is the canonical example for teaching the pitfalls of backtesting. In practice, a developer building a price-forecasting model for a trading desk would use a library like `statsmodels` for ARIMA or a gradient boosting library like `XGBoost` with features like lagged returns and volume. The most important code they write is not the model but the data split: they must ensure that training data ends before validation data and that test data comes even later. The common failure is using `train_test_split` from scikit-learn without shuffling, which randomly mixes dates and leaks future information into training. A developer must write a custom split that keeps time order, perhaps using `TimeSeriesSplit` from scikit-learn. When done badly, a model can show a 90% accuracy on the shuffled test set but then lose money in live trading because the shuffled test set had future data that the model latched onto. This is why the discipline of temporal splits and out-of-sample evaluation is the core lesson — not the model architecture.


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Read this on the web: https://basavapurushottam.com/learn-ai/stock-price-prediction
